1. Field of the Invention
The present invention relates to a manipulator simulation method and apparatus adapted to evaluate angles of rotation of joints for coupling arm-to-arm to each other on the basis of information representative of position and attitude or orientation of a tip of a manipulator having six or less arms, which are sequentially coupled with each other, so as to implement the position and the attitude or orientation of the tip of the manipulator.
2. Description of the Related Art
FIG. 9 is a typical illustration of an example of a manipulator comprising a plurality of arms and joints for coupling the arms to each other.
In FIG. 9, a plurality of arms 2.sub.-- 1, 2.sub.-- 2, . . . , 2.sub.-- 5 are sequentially coupled with each other by joints 3.sub.-- 1, 3.sub.-- 2, . . . , 3.sub.-- 5 on a substrate or a base 1. A hand 4 is coupled with the top arm 2.sub.-- 5. The hand 4 serves to grasp a work object 5 and let loose the same through switching of a finger 4a constituting the hand 4. The joints 3.sub.-- 1, 3.sub.-- 2, . . . , 3.sub.-- 5 are arranged in such a manner that the arms 2.sub.-- 1, 2.sub.-- 2, . . . , 2.sub.-- 5 coupled with each other by joints 3.sub.-- 1, 3.sub.-- 2, . . . , 3.sub.-- 5 are rotatably movable. The use of such a manipulator makes it possible to perform, through a rotatable movement of the arms such that the hand 4 of the tip of the arms 2.sub.-- 1, 2.sub.-- 2, . . . , 2.sub.-- 5 is in a predetermined position and takes a predetermined attitude, a work, for example, such that the work object 5 is grasped and carried to another position.
It is referred to as the inverse kinematics that in the manipulator arranged, for example, as illustrated in FIG. 9, information as to the position and orientation of the tip of the manipulator is provided, so that angles of the respective joints are evaluated to move the tip of the manipulator to the given position with the given attitude.
Such inverse kinematics are applicable to the following fields
(1) Robots
For a robot having an arbitrary link configuration, the inverse kinematics is automatically solved, so that applications to the work plans of the robot are facilitated.
(2) CAD systems for a mechanism design
Incorporation of the inverse kinematics into the CAD system for a mechanism design, in which a design for parts having a link mechanism is often performed, makes it possible to simulate beforehand as to whether products having the link mechanism operate as desired.
(3) Production of an animation in the multimedia
In the multimedia, various applications in mixing of computer graphics, video and audio are expected. On the other hand, in the field of the commercial and a movie, it is desired to produce an animation, which is high in reality, using the computer graphics. Hitherto, in the field of the computer graphics, the animation is produced on an off-line basis. Particularly, with regard to a motion for an android model, there have been adopted a very troublesome scheme in which an angle is designated for each joint and a motion capturing scheme in which a specific sensor is attached to the human body so as to take in the motion into a computer. Incorporation of the inverse kinematics into an animation producing tool makes it possible to very efficiently produce a motion of the animation model such as the android.
(4) Ergonomics
Hitherto, in a design of products having some contact with the human, such as chairs, desks, keyboards and the like, there is seen a lack of arguments as to the readiness-to-use, the operability, and the amenity on an ergonomics basis. It is noted, however, that incorporation of the inverse kinematics into the android model produced by the computer graphics makes it possible to perform an inspection of manufactured goods through various motions of the android model at the stage of the simulation.
Hitherto, in connection with the problem of the inverse kinematics, in a case where analytic solutions exist, an algebraic operation is performed one by one for each object to evaluate the analytic solution. In this case, it is difficult to discriminate between the case of the existence of the analytic solution and the case of the non-existence of the analytic solution. This involves a lack of generality for a system in its entirety. Further, in a design, even a manipulator having the analytic solutions, when such a manipulator is manufactured indeed, it happens that the calibration involves a minor offset and as a result the inverse kinematics with the analytic solution is not useful.
On the other hand, in connection with the case of non-existence of the analytic solution, there has been developed a method referred to as a homotopy scheme or a continuation scheme in which the precision is improved by means of repeating the numerical solution starting from the approximate solution, specifically, constituting a predictor-corrector on a Newton-Raphson basis.
This method involves, however, the following drawbacks and cannot be used practically.
(1) There is a case where numerical instability exists.
(2) There is not seen dependency to the physical constant (D-H parameter).
(3) A calculation load is large.